Expert: Daniel Mazur - 10/18/2005

Question
Dear expert,
  I am doing a science fair project on motion and I was wondering if you could help me. My purpose for my science fair project is, does the surface of an area affect the height a ball will bounce? I was told that I am not testing the bounce but the surfaces (wood, cement, dirt, and sand) and using the ball and the bounce for the tests. If you could help me, I would really appreciate that by sending me information on the subject or by sending me a link or book to find information. Thank you for your time. If you can send me information please send it to bigkev2004@sbcglobal.net. Thank  you again.
                                                                          Sincerely,
                           Kevin

Answer
Hi Kevin,

I do not understand to task completely, I do not know, what you meant by "surface of an area". If you meant "material of the surface", then the answer is generally yes. A ball will generally bounce to different heights when bouncing of different materials.

If you are familiar with the Energy Conservation Law, you see that it is the energy dissipation (inelastic loss) at the moment of ball impact, that determines the bounce height. This dissipation depends on the choice of materials of the ball and the "floor", too. You can try the experiment with "extreme" materials to see the effect:
Tennis ball on clay/mud or sand -> nearly zero bounce height
Clay ball on concrete -> zero bounce height
Tennis ball on concrete -> bounces to ~70% of original height

What you must understand before doing the experiment, it is not only the choice of the surface materials, but the choice of material untill a certain depth (this depth depends on the material). If you take concrete floor, do the experiment and then just sprinkle a little dirt or sand on top of the concrete and repeat the experiment, the two results will not be much different. If you keep on adding the amount of sand millimeter by millimeter and repeat the experiment after each run, you will be able to observe the bounce height go down to zero gradually. In other words, the amount of energy dissipated in the impact imcreases from the value for clean concrete to the value of a bucket of sand. So, it is not quite the surface that affects the result, it is the "bulk" of the material.

Secondly, I should tell you that your experiment is NOT one that studies motion. It does not even use the motion in the proper sense, because you are measuring static variables only (height), no dynamic ones (an example would be velocity). You are using only static force (gravity) and presumably are looking at the ball impact time as an "instant", as opposed to studying the dynamics of momentum transfer during the (short but non-zero) period of impact.

Instead, your experiment studies the inelastic properties of materials of the ball and the floor. This does not have to put you down, it does not destroy the experiment. I only wanted you to see, what the experiment is REALLY about and what is the cotton ball around.

As far as recommendation of resources goes, I reckon any textbook of Mechanics will do the job. You will need to look for 'energy' and 'dissipation' keywords and the relation between kinetic energy and potential energy of gravitational field on Earth's surface. All this is in the basic textbooks. When it comes to properties of materials, you will have to sink deeper into the subject of elasticity and impact dynamics (for example the problem, why karate men can break harder objects easier than softer/more elastic ones) to get the correct idea. I don't know, what level you are at (you didn't write it to me), so I cannot help you more.

Still I hope this helped.
Good luck!
Daniel